The embattled leader of the Democratic Unionists in Northern Ireland, Arlene Foster, will remain in her post despite her party losing 10 seats in Thursday’s election to the devolved assembly in Belfast, one of her MPs has said.

Jeffrey Donaldson insisted that instead of seeking her resignation the focus should be “on Arlene and the party getting a government up and running again at Stormont”.

Sinn Féin is now only one seat behind the DUP after a bruising and divisive election caused by Foster’s refusal to temporarily stand down as Northern Ireland’s first minister following a botched green energy scheme scandal which has the potential of costing taxpayers £500m.

Gerry Adams, Sinn Féin’s president, said late on Saturday that the election result, which saw his party move up to 27 seats, showed “the notion of a perpetual unionist majority has been demolished” in Northern Ireland. Speaking earlier in West Belfast, Adams described Sinn Féin’s performance as a “watershed moment.”

The DUP remain the largest party in the new assembly, with Donaldson stressing that Foster would still be their nominee as first minister if and when a power-sharing government is restored.

Donaldson said: “I am not aware of any election in the past where the leader of the largest party resigns because they have won the election.

“We need to learn the lesson and understand what people were saying in this election and what the key messages are. We have been given the responsibility as the main party to take the lead at Stormont and that is what we intend to do, so we are not going to get bogged down on what some people want to focus on, which is personalities.”

Northern Ireland assembly election: final results

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The election results mean the DUP and Sinn Féin will once again lead the negotiations aimed at creating a new power-sharing government in Belfast when they take place on Monday. However, the prospect of the parties reaching agreement in the three-week timeframe imposed by the Northern Ireland secretary, James Brokenshire, appears remote.

If that deadline passes, the government would be obliged to call yet another snap election, but it may instead opt to put Stormont in cold storage and reintroduce direct rule.

Before the negotiations start on Monday the Irish government has been contacting all of the parties over the weekend to persuade them to reach a deal.

In a statement on Saturday night, Ireland’s foreign minister, Charlie Flanagan, said the high 65% turnout at the election demonstrated that people in the north cared about the institutions set up under the 1998 Good Friday agreement and the devolved government.

Flanagan said: “As co-guarantors of the Good Friday agreement and subsequent agreements, the Irish and British governments stand ready to provide whatever support or engagement may be necessary to re-establish the devolved institutions. In this regard, I plan to be in touch with the parties in Northern Ireland and with Secretary of State Brokenshire over the next 24 hours.”

Earlier on Saturday, the Northern Ireland secretary also claimed that the election results proved that people in the region wanted cross-community devolved government back in place.

Former first minister urges NI parties not to destroy devolution

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Brokenshire called for “intensive” negotiations between the parties to begin on Monday morning. He insisted his prime goal was to see power-sharing devolution restored rather than the imposition of direct rule.

“Northern Ireland has made great strides forward over the past two decades,” he said. “All of us must continue the work of building a stable, peaceful and prosperous Northern Ireland that works for everyone, based on the strong foundations of the Belfast agreement and its successors.

“It is with positive intent that the UK government approaches the days ahead. I will be speaking to party leaders during the course of today and remaining in contact with the Irish government.”

The DUP took a major electoral hit over the controversy around a renewable heat incentive scheme that became known as the “cash for ash” scandal. Owing to poor accounting, the incentive resulted in farmers and small businesses making £1.60 for every £1 they invested in boilers fired with wood pellets and other recyclable materials. It will now cost taxpayers in Northern Ireland an estimated £500m. The DUP was criticised first for championing the scheme through Foster, and then for defending the project despite the spiralling cost to the public purse.

All 90 seats were declared on Saturday morning with 28 to the DUP, Sinn Féin on 27, the SDLP with 12, the Ulster Unionists falling to 10, the cross-community Alliance party with eight, the Green party securing two, the hardline Traditional Unionist Voice coming back with one seat and the leftwing People Before Profit party going down to one. The Independent Unionist and justice minister in the last coalition, Clare Sugden, was also re-elected.

• This article was amended on 6 March 2017. An earlier version stated the potential cost of the green energy scheme as both £500,000 and £500m; the latter is correct.